Poisson geometry of certain moduli spaces

Huebschmann, Johannes

Displaying similar documents to “Poisson geometry of certain moduli spaces”

Poisson structures on certain moduli spaces for bundles on a surface

Johannes Huebschmann (1995)

Annales de l'institut Fourier

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Let $Σ$ be a closed surface, $G$ a compact Lie group, with Lie algebra $g$ , and $ξ : P \to Σ$ a principal $G$ -bundle. In earlier work we have shown that the moduli space $N (ξ)$ of central Yang-Mills connections, with reference to appropriate additional data, is stratified by smooth symplectic manifolds and that the holonomy yields a homeomorphism from $N (ξ)$ onto a certain representation space ${Rep}_{ξ} (Γ, G)$ , in fact a diffeomorphism, with reference to suitable smooth structures $C^{\infty} (N (ξ))$ and $C^{\infty} ({Rep}_{ξ} (Γ, G))$ , where $Γ$ denotes the universal central...

Gauge equivalence of Dirac structures and symplectic groupoids

Henrique Bursztyn, Olga Radko (2003)

Annales de l’institut Fourier

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We study gauge transformations of Dirac structures and the relationship between gauge and Morita equivalences of Poisson manifolds. We describe how the symplectic structure of a symplectic groupoid is affected by a gauge transformation of the Poisson structure on its identity section, and prove that gauge-equivalent integrable Poisson structures are Morita equivalent. As an example, we study certain generic sets of Poisson structures on Riemann surfaces: we find complete gauge-equivalence...

Abstract mechanical connection and Abelian reconstruction for almost Kähler manifolds.

Pekarsky, Sergey, Marsden, Jerrold E. (2001)

Journal of Applied Mathematics

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Deformation quantization

Alan Weinstein (1993-1994)

Séminaire Bourbaki

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Hyper-Lie Poisson structures

Ping Xu (1997)

Annales scientifiques de l'École Normale Supérieure

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Spectral curves and integrable systems

Eyal Markman (1994)

Compositio Mathematica

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Aspects of Geometric Quantization Theory in Poisson Geometry

Izu Vaisman (2000)

Banach Center Publications

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This is a survey exposition of the results of [14] on the relationship between the geometric quantization of a Poisson manifold, of its symplectic leaves and its symplectic realizations, and of the results of [13] on a certain kind of super-geometric quantization. A general formulation of the geometric quantization problem is given at the beginning.